What is the sum of odd numbers from 22 to 172? Here we will show you step-by-step how to calculate the sum of odd numbers from 22 to 172.
Step 1) We start by finding the first (F) and last (L) odd numbers from 22 to 172. It is easy to do that by simply looking at the numbers. The first odd number is 23, and the last odd number is 171.
F = 23
L = 171
Step 2) Next, we calculate the total odd numbers (T) there are from 22 to 172, using a formula. Here is the formula and the math:
T = (L - F + 2) ÷ 2
T = (171 - 23 + 2) ÷ 2
T = 150 ÷ 2
T = 75
Step 3) Finally, we use the information from Step 1 and Step 2, and another formula, to calculate the sum of odd numbers from 22 to 172, like this:
Sum = (T ÷ 2) × (2 × F + (2 × (T - 1))
Sum = (75 ÷ 2) × (2 × 23 + (2 × (75 - 1))
Sum = 37.5 × (46 + 148)
Sum = 37.5 × 194
Sum = 7275
Sum of odd numbers from 22 to 172 = 7275
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